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The behaviour of rarefied monatomic gas of Maxwell particles within a rectangular enclosure is investigated, with the Navier–Stokes and Fourier field of equations with first- (NSF) and second-order boundary conditions (NSF2) of the velocity slip and temperature jump, and the regularized 13 moments approach (R13). The enclosure considered has a heated bottom with lateral walls that have specular reflection. The effect of the three dimensionless parameters characterizing the simulated problem, the cavity aspect ratio, the Knudsen number, and the temperature ratio of the hot over the cold walls, on the flow and bulk quantities is examined. For the small Knudsen numbers the flow presents one type of streamlines from the cold to hot plate in both NSF and R13 theories, while by increasing the Knudsen number the flow becomes more complex and presents hot to cold flow streamlines in the extended approach of R13. These rarefaction effects cannot be predicted by the classical continuum approach of NSF. The increase of the temperature ratio in R13 affects the hot to cold flow, which begins to vanish, while this type of streamline does not appear by decreasing the aspect ratio.

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In this paper, the regularized 13‐moment approach (R13) is used to investigate the rarefaction effect on rarefied gas flow within a lid‐driven cavity. We will discuss the validity domain of the Navier‐Stokes and Fourier (NSF) solutions using the first order of velocity slip and temperature jump boundary conditions (NSF) and the regularized 10‐moments (R10) in slip and early transition regime. The effect of an external body force is examined in different directions according to the cavity inclination angle. A Maxwell monatomic gas is considered to study the flow and thermal characteristics within the lid‐driven cavity. The NSF method correctly describes the velocity profiles, but it captures only the trend of other macroscopic parameters. The NSF heat flux, which is found to be from the hot regions to the cold ones, loses its validity in the slip regime and beyond to predict an inverted heat flux predicted by both regularized models. Contrary to the R10, which can capture the rarefaction effect in the whole slip regime. The dimensionless shear stress tends to grow by increasing the rarefaction along the moving wall. The external body force affects the shear stress and velocity streamlines symmetry and creates an additional vortex, depending on the inclination angle.

The behaviour of monatomic and dilute gas is studied in the slip and early transition regimes using the extended macroscopic theory. The gas is confined within a two-dimensional microcavity where the longitudinal sides are in the opposite motion with constant velocity ±Uw. The microcavity walls are kept at the uniform and reference temperature T0. Thus, the gas flow is transported only by the shear stress induced by the motion of upper and lower walls. From the macroscopic point of view, the regularized 13-moment equations of Grad, R13, are solved numerically. The macroscopic gas proprieties are studied for different values of the so-called Knudsen number (Kn), which gives the gas-rarefaction degree. The results are compared with those obtained using the classical continuum theory of Navier-Stokes and Fourier (NSF).